Learn Multiplication

Adding a certain number of objects again and again is Multiplication. Multiplication means Counting by number. Counting by 2's means 2, 4, 6, 8... and so on Similarly Counting by 5's means 5, 10, 15, 20...and so on

Product : - When two numbers are multiplied, the result/answer is called product. Ths product also tells how many there are in all.

Example
 Total number of chocolates are 10

Explanation:

This can be written in different ways:

a) Five chocolates + five chocolates
b) The number 5 taken 2 times.
c) 5×2=10. Total number of chocolates are 10.

Note:

  •  Multiplication is represented by the ‘×’ sign.
  •  The result is shown after equal ‘=’ sign.

For example, I have 4 red apples in one group and 4 green apples in other group. How many are there in all 4 + 4 = 8 or 2 * 4 = 8 Here the number or digit 2 and 4 are called Operands The multiply or "*" is called operator. whereas the number 8 is the product. Similarly, 3 + 3 + 3 + 3 = 12 or 3 * 4 = 12


Simple multiplications


Example:
 16

Explanation:

Stars in each row - 4
Number of rows - 4
Total number of stars = the number 4 taken 4 times.
So that, 4 × 4 = 16
4 + 4 + 4 + 4 = 4 × 4 = 16
Total number of stars = 16

Simple Multiplication


Multiplications without carrying over


Simple Example


 84

Explanation:

First arrange the multiplication vertically.
Now multiply the units digit 2 in 42 by 2.
Write the product 4 in the units place.
Multiply the tens digit 4 in 42 by 2.
Write the product 8 in the tens place.
Hence, 42 × 2 = 84

Multiplications without carrying over


Multiplication : Word Problems


 $ 444

Explanation:

Number of books 2.
To find out total cost of books multiply 222 with 2.
First arrange the multiplication vertically.
Now multiply the units digit 2 in 222 by 2.
Write the product 4 in the units place.
Multiply the tens digit 2 in 222 by 2.
Write the product 4 in the tens place.
Multiply the hundreds digit 2 in 222 by 2.
Write the product 4 in the hundreds place.
Hence, 222 × 2 = 444
The cost of 4 such notebooks $ 444

Multiplication without carrying over


Multiplications with carrying over


Simple Example

 588

Explanation:

First arrange the multiplication vertically.
Now multiply the units digit 4 in 84 by 7.
The product is 28.
Write the product 8 units from 28 in the units place.
Carry over the 2 tens from 28 to the tens column.
Multiply the tens digit 8 in 84 by 7.
The product is 56.
56T + 2T = 58T
Write the product 8 tens from 58 in the tens place.
Carry over the 5 hundreds from 58 to the hundreds column.
Write 5 in the hundreds place.
Hence, 84 × 7 = 588

Multiplication with carrying over


Multiplication : Word Problems


Example 1:
If 57 trees are planted in each row, then how many such trees are there in 7 rows?
 399

Explanation:

Number of trees 57.
To find out total number of trees multiply 57 with 7.

First arrange the multiplication vertically.
Now multiply the units digit 7 in 57 by 7.
The product is 49.
Write the product 9 units from 49 in the units place.
Carry over the 4 tens from 49 to the tens column.
Multiply the tens digit 5 in 57 by 7.
The product is 35.
35T + 4T = 39T
Write the product 9 tens from 39 in the tens place.
Carry over the 3 hundreds from 39 to the hundreds column.
Write 3 in the hundreds place.
Hence, 57 × 7 = 399

Multiplication with carrying over

Example 2:
On a grand feast there are many people invited from different countries. Tables were arranged as 250 people can get a seat in each row for a dinner. How many guests would be arranged in 25 such rows for a dinner?
 Total 6250 guests were arranged for a dinner.

Explanation:

Number of rows = 25
To find the total guests can be seat in 25 rows, multiply 250 with 25.
So that, 250 × 25
First arrange the multiplication vertically.
First multiply 250 with the unit place of multiplier which is 5.
Now multiply the units digit 0 in 250 by 5.
The product is 0.
Multiply the tens digit 5 in 250 by 5.
The product is 25.
Write 5 in tens place and Carry over 2 to the hundreds column.
Multiply the hundreds digit 2 in 250 by 5.
The product is 10. 10H + 2H = 12H
Write 12 in hundreds place.
Hence, 250 × 5 = 1250
After 250 is multiplied by 5, 250 is multiplied by the tens place of the multiplier which is 2.
Multiply 250 by 2. Write the product below the first answer we got that was 1250. The product will move one place to the left. We can write 0 in the unit place to be more convenient with it.
Hence, 250 × 2 = 5000
Add the two products together to get a final answer.
So that, 1250 + 5000 = 6250
Hence, 250 × 25 = 6250

Multiplication with carrying over


Properties of multiplication


Commutativity


When two numbers are multiplied together order does not matter.

So that, a × b= b × a

For example, 5 × 9

  •  5 × 9 = 45
  •  If we reverse the order of this numbers as we say, 9 × 5 is also 45
  •  So that, 5 × 9 = 9 × 5 = 45

Associativity


When three or more numbers are multiplied together, For any three numbers a, b, and c, (a × b) × c = a × (b × c).

For example, (1 × 3) × 4=?

  •  (1 × 3) × 4 = 3 × 4 = 12
  •  Now 12 = 1 × 12 = 1 × (3 × 4)
  •  so that, (1 × 3) × 4= 1 × (3 × 4)

Distributive property


For any three numbers a, b, and c, a × (b+ c) = (a × b ) + (a × c)

For example,5× (3+ 4) =?

  •  5× (3+ 4) = 5× 7= 35
  •  Now 35 = 15+20 = (5× 3) + (5 × 4)
  •  So that, 5× (3+ 4) = ( 5× 3) + (5 × 4)

Identity element


If any number is multiplied by one the result will be same as itself.
So that, a×1= a

For example, (1 × 3) = 3


Zero element


If any number is multiplied by zero the result will be zero.
So that, a × 0 = 0
For example, (100 × 0) = 0


Fact family multiplication


If we multiply two numbers in any order we get the same product.
For example 5 multiplied by 7 is 35 as well as 7 multiplied by 5 is 35. The numbers 5, 7 and 35 forms fact family.

 Points to Remember

Quick Tips

  •  We should always start to multiply the numbers from unit place of the given number.
  •  Order does not matter when we multiply too many numbers together.
  •  When multiplier is more than one digit number first start to multiply by units place. Move one place left every time and write the product below to the first product. Add all products together to get the final answer.

Think

  •  A spider has 8 legs. How many legs do 7 spiders have?
  •  What is 20,000 × 1 and 20,000 × 0?
  •  Meena has 25 chocolates. Trush has 5 times more than her. How many chocolates does Trush have?
  •  What happens when you multiply by 0?
  •  what happens when you change the order of operands in multiplication?





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